mirror of
https://github.com/c3lang/c3c.git
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511 lines
12 KiB
Plaintext
511 lines
12 KiB
Plaintext
module std::math::math_rt;
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fn int128 __divti3(int128 a, int128 b) @cname("__divti3") @weak @nostrip
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{
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int128 sign_a = a >> 127; // -1 : 0
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int128 sign_b = b >> 127; // -1 : 0
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uint128 unsigned_a = (uint128)(a ^ sign_a) + (-sign_a);
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uint128 unsigned_b = (uint128)(b ^ sign_b) + (-sign_b);
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sign_a ^= sign_b; // quotient sign
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return __udivti3(unsigned_a, unsigned_b) @inline ^ sign_a + (-sign_a);
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}
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macro uint128 @__udivmodti4(uint128 a, uint128 b, bool $return_rem)
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{
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Int128bits n = { .all = a };
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Int128bits d = { .all = b };
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Int128bits q @noinit;
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Int128bits r @noinit;
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uint sr;
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if (n.high == 0)
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{
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if (d.high == 0)
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{
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$if $return_rem:
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return n.low % d.low;
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$else
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return n.low / d.low;
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$endif
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}
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$if $return_rem:
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return n.low;
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$else
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return 0;
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$endif
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}
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if (d.low == 0)
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{
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if (d.high == 0)
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{
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$if $return_rem:
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return n.high % d.low;
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$else
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return n.high / d.low;
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$endif
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}
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if (n.low == 0)
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{
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$if $return_rem:
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r.high = n.high % d.high;
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r.low = 0;
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return r.all;
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$else
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return n.high / d.high;
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$endif
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}
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if (d.high & (d.high - 1) == 0) // d is pot
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{
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$if $return_rem:
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r.low = n.low;
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r.high = n.high & (d.high - 1);
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return r.all;
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$else
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return (uint128)(n.high >> $$ctz(d.high));
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$endif
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}
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sr = (uint)$$clz(d.high) - (uint)$$clz(n.high);
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// 0 <= sr <= n_udword_bits - 2 or sr large
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if (sr > 64 - 2)
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{
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$if $return_rem:
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return n.all;
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$else
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return 0;
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$endif
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}
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sr++;
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// 1 <= sr <= n_udword_bits - 1
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// q.all = n.all << (n_utword_bits - sr);
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q.low = 0;
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q.high = n.low << (64 - sr);
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r.high = n.high >> sr;
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r.low = (n.high << (64 - sr)) | (n.low >> sr);
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}
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else // d.s.low != 0
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{
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if (d.high == 0)
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{
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if (d.low & (d.low - 1) == 0) // if d is a power of 2
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{
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$if $return_rem:
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return (uint128)(n.low & (d.low - 1));
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$else
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if (d.low == 1) return n.all;
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sr = (uint)$$ctz(d.low);
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q.high = n.high >> sr;
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q.low = (n.high << (64 - sr)) | (n.low >> sr);
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return q.all;
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$endif
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}
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sr = 1 + 64 + (uint)$$clz(d.low) - (uint)$$clz(n.high);
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// 2 <= sr <= n_utword_bits - 1
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// q.all = n.all << (n_utword_bits - sr);
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// r.all = n.all >> sr;
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switch
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{
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case sr == 64:
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q.low = 0;
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q.high = n.low;
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r.high = 0;
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r.low = n.high;
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case sr < 64:
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q.low = 0;
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q.high = n.low << (64 - sr);
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r.high = n.high >> sr;
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r.low = (n.high << (64 - sr)) | (n.low >> sr);
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default: // n_udword_bits + 1 <= sr <= n_utword_bits - 1
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q.low = n.low << (128 - sr);
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q.high = (n.high << (128 - sr)) | (n.low >> (sr - 64));
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r.high = 0;
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r.low = n.high >> (sr - 64);
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}
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}
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else
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{
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sr = (uint)$$clz(d.high) - (uint)$$clz(n.high);
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// 0 <= sr <= n_udword_bits - 1 or sr large
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if (sr > 64 - 1)
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{
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$if $return_rem:
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return n.all;
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$else
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return 0;
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$endif
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}
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sr++;
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// 1 <= sr <= n_udword_bits
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// q.all = n.all << (n_utword_bits - sr);
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// r.all = n.all >> sr;
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q.low = 0;
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if (sr == 64)
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{
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q.high = n.low;
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r.high = 0;
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r.low = n.high;
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}
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else
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{
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r.high = n.high >> sr;
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r.low = (n.high << (64 - sr)) | (n.low >> sr);
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q.high = n.low << (64 - sr);
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}
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}
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}
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// Not a special case
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// q and r are initialized with:
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// q.all = n.all << (128 - sr);
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// r.all = n.all >> sr;
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// 1 <= sr <= n_utword_bits - 1
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uint carry = 0;
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for (; sr > 0; sr--)
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{
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// r:q = ((r:q) << 1) | carry
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r.high = (r.high << 1) | (r.low >> (64 - 1));
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r.low = (r.low << 1) | (q.high >> (64 - 1));
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q.high = (q.high << 1) | (q.low >> (64 - 1));
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q.low = (q.low << 1) | carry;
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// carry = 0;
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// if (r.all >= d.all)
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// {
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// r.all -= d.all;
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// carry = 1;
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// }
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int128 s = (int128)(d.all - r.all - 1) >> (128 - 1);
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carry = (uint)(s & 1);
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r.all -= d.all & s;
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}
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$if $return_rem:
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return r.all;
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$else
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return (q.all << 1) | carry;
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$endif
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}
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fn uint128 __umodti3(uint128 n, uint128 d) @cname("__umodti3") @weak @nostrip
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{
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return @__udivmodti4(n, d, true);
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}
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fn uint128 __udivti3(uint128 n, uint128 d) @cname("__udivti3") @weak @nostrip
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{
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return @__udivmodti4(n, d, false);
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}
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fn int128 __modti3(int128 a, int128 b) @cname("__modti3") @weak @nostrip
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{
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int128 sign = b >> 127;
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uint128 unsigned_b = (uint128)(b ^ sign) + (-sign);
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sign = a >> 127;
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uint128 unsigned_a = (uint128)(a ^ sign) + (-sign);
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return __umodti3(unsigned_a, unsigned_b) ^ sign + (-sign);
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}
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union Int128bits @private
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{
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struct
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{
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ulong low;
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ulong high;
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}
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uint128 all;
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}
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fn uint128 __lshrti3(uint128 a, uint b) @cname("__lshrti3") @weak @nostrip
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{
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Int128bits result;
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result.all = a;
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if (b >= 64)
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{
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result.low = result.high >> (b - 64);
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result.high = 0;
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}
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else
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{
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if (b == 0) return a;
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result.low = (result.high << (64 - b)) | (result.low >> b);
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result.high = result.high >> b;
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}
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return result.all;
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}
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fn int128 __ashrti3(int128 a, uint b) @cname("__ashrti3") @weak @nostrip
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{
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Int128bits result;
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result.all = a;
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if (b >= 64)
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{
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result.low = result.high >> (b - 64);
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result.high = result.high >> 63;
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}
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else
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{
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if (b == 0) return a;
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result.low = result.high << (64 - b) | (result.low >> b);
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result.high = result.high >> b;
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}
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return result.all;
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}
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fn int128 __ashlti3(int128 a, uint b) @cname("__ashlti3") @weak @nostrip
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{
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Int128bits result;
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result.all = a;
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if (b >= 64)
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{
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result.low = 0;
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result.high = result.low << (b - 64);
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}
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else
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{
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if (b == 0) return a;
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result.high = (result.high << b) | (result.low >> (64 - b));
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result.low = result.low << b;
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}
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return result.all;
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}
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// Returns: a * b
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fn int128 __mulddi3(ulong a, ulong b) @private
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{
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Int128bits r;
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const ulong LOWER_MASK = 0xffff_ffff;
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r.low = (a & LOWER_MASK) * (b & LOWER_MASK);
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ulong t = r.low >> 32;
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r.low &= LOWER_MASK;
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t += (a >> 32) * (b & LOWER_MASK);
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r.low += (t & LOWER_MASK) << 32;
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r.high = t >> 32;
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t = r.low >> 32;
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r.low &= LOWER_MASK;
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t += (b >> 32) * (a & LOWER_MASK);
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r.low += (t & LOWER_MASK) << 32;
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r.high += t >> 32;
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r.high += (a >> 32) * (b >> 32);
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return r.all;
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}
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fn int128 __multi3(int128 a, int128 b) @cname("__multi3") @weak @nostrip
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{
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Int128bits x = { .all = a };
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Int128bits y = { .all = b };
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Int128bits r = { .all = __mulddi3(x.low, y.low) };
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r.high += x.high * y.low + x.low * y.high;
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return r.all;
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}
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fn float __floattisf(int128 a) @cname("__floattisf") @weak @nostrip => float_from_i128(float, a);
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fn double __floattidf(int128 a) @cname("__floattidf") @weak @nostrip => float_from_i128(double, a);
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fn float __floatuntisf(uint128 a) @cname("__floatuntisf") @weak @nostrip => float_from_u128(float, a);
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fn double __floatuntidf(uint128 a) @cname("__floatuntidf") @weak @nostrip => float_from_u128(double, a);
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fn uint128 __fixunsdfti(double a) @weak @cname("__fixunsdfti") @nostrip => fixuint(a);
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fn uint128 __fixunssfti(float a) @weak @cname("__fixunssfti") @nostrip => fixuint(a);
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fn int128 __fixdfti(double a) @weak @cname("__fixdfti") @nostrip => fixint(a);
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fn int128 __fixsfti(float a) @weak @cname("__fixsfti") @nostrip => fixint(a);
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macro float_from_i128($Type, a) @private
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{
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var $Rep;
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$switch $Type:
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$case double:
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$Rep = ulong;
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const MANT_DIG = math::DOUBLE_MANT_DIG;
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const SIGNIFICANT_BITS = 52;
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const EXP_BIAS = 1023;
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const MANTISSA_MASK = 0xFFFFF_FFFF_FFFFUL;
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const SIGN_BIT = 1UL << 63;
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$case float:
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$Rep = uint;
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const MANT_DIG = math::FLOAT_MANT_DIG;
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const EXP_BIAS = 127;
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const SIGNIFICANT_BITS = 23;
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const MANTISSA_MASK = 0x7F_FFFFU;
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const SIGN_BIT = 1U << 31;
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$case float16:
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$Rep = ushort;
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const MANT_DIG = math::HALF_MANT_DIG;
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$case float128:
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$Rep = uint128;
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const MANT_DIG = QUAD_MANT_DIG;
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$endswitch
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if (a == 0) return ($Type)0;
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// Grab and remove sign.
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int128 sign = a >> 127;
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a = (a ^ sign) - sign;
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int sd = 128 - (int)$$clz(a); // digits
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int e = sd - 1; // exponent
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if (sd > MANT_DIG)
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{
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switch (sd)
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{
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case MANT_DIG + 1:
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a <<= 1;
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case MANT_DIG + 2:
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break;
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default:
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a = (a >> (sd - (MANT_DIG + 2)))
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| (uint128)((a & ((uint128)(-1) >> ((128 + MANT_DIG + 2) - sd))) != 0);
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}
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a |= (uint128)((a & 4) != 0);
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a++;
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a >>= 2;
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if (a & (1LL << MANT_DIG))
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{
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a >>= 1;
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e++;
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}
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}
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else
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{
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a <<= (MANT_DIG - sd);
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}
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return bitcast((($Rep)sign & SIGN_BIT) | ((($Rep)e + ($Rep)EXP_BIAS) << SIGNIFICANT_BITS) | (($Rep)a & ($Rep)MANTISSA_MASK), $Type);
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}
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macro float_from_u128($Type, a) @private
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{
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var $Rep;
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$switch $Type:
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$case double:
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$Rep = ulong;
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const MANT_DIG = math::DOUBLE_MANT_DIG;
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const SIGNIFICANT_BITS = 52;
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const EXP_BIAS = 1023;
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const MANTISSA_MASK = 0xFFFFF_FFFF_FFFFUL;
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$case float:
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$Rep = uint;
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const MANT_DIG = math::FLOAT_MANT_DIG;
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const EXP_BIAS = 127;
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const SIGNIFICANT_BITS = 23;
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const MANTISSA_MASK = 0x7F_FFFFU;
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$case float16:
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$Rep = ushort;
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const MANT_DIG = math::HALF_MANT_DIG;
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$case float128:
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$Rep = uint128;
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const MANT_DIG = math::QUAD_MANT_DIG;
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$endswitch
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if (a == 0) return ($Type)0;
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int sd = 128 - (int)$$clz(a); // digits
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int e = sd - 1; // exponent
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if (sd > MANT_DIG)
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{
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switch (sd)
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{
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case MANT_DIG + 1:
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a <<= 1;
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case MANT_DIG + 2:
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break;
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default:
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a = (a >> (sd - (MANT_DIG + 2)))
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| (uint128)((a & ((uint128)(-1) >> ((128 + MANT_DIG + 2) - sd))) != 0);
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}
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a |= (uint128)((a & 4) != 0);
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a++;
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a >>= 2;
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if (a & (1LL << MANT_DIG))
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{
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a >>= 1;
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e++;
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}
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}
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else
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{
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a <<= (MANT_DIG - sd);
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}
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return bitcast(((($Rep)e + ($Rep)EXP_BIAS) << SIGNIFICANT_BITS) | (($Rep)a & ($Rep)MANTISSA_MASK), $Type);
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}
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macro fixuint(a) @private
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{
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var $Rep;
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$switch $typeof(a):
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$case double:
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$Rep = ulong;
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const EXPONENT_BITS = 11;
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const SIGNIFICANT_BITS = 52;
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$case float:
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$Rep = uint;
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const EXPONENT_BITS = 8;
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const SIGNIFICANT_BITS = 23;
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$case float16:
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$Rep = ushort;
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const EXPONENT_BITS = 5;
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const SIGNIFICANT_BITS = 10;
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$case float128:
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$Rep = uint128;
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const EXPONENT_BITS = 15;
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const SIGNIFICANT_BITS = 112;
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$endswitch
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const $Rep MAX_EXPONENT = ($Rep)1 << EXPONENT_BITS - 1u;
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const $Rep EXPONENT_BIAS = MAX_EXPONENT >> 1u;
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const $Rep ONE_REP =EXPONENT_BIAS << SIGNIFICANT_BITS;
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const $Rep SIGN_BIT = ($Rep)1 << (EXPONENT_BITS + SIGNIFICANT_BITS);
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const $Rep ABS_MASK = SIGN_BIT - 1u;
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const $Rep IMPLICIT_BIT = ($Rep)1 << SIGNIFICANT_BITS;
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const $Rep SIGNIFICANT_MASK = IMPLICIT_BIT - 1u;
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const $Rep EXPONENT_MASK = ABS_MASK ^ SIGNIFICANT_MASK;
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const $Rep QUIET_BIT = IMPLICIT_BIT >> 1;
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const $Rep QNAN_REP = EXPONENT_MASK | QUIET_BIT;
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const $Rep INF_REP = EXPONENT_MASK;
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$Rep rep = bitcast(a, $Rep);
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$Rep abs = rep & ABS_MASK;
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int sign = rep & SIGN_BIT ? -1 : 1;
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int exponent = (int)((abs >> SIGNIFICANT_BITS) - EXPONENT_BIAS);
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$Rep significand = (abs & SIGNIFICANT_MASK) | IMPLICIT_BIT;
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if (sign == -1 || exponent < 0) return 0ULL;
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if ((uint)exponent >= uint128.sizeof * 8) return ~0ULL;
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if (exponent < SIGNIFICANT_BITS) return (uint128)significand >> (SIGNIFICANT_BITS - exponent);
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return (uint128)significand << (exponent - SIGNIFICANT_BITS);
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}
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macro fixint(a) @private
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{
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var $Rep;
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$switch $typeof(a):
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$case double:
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$Rep = ulong;
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const EXPONENT_BITS = 11;
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const SIGNIFICANT_BITS = 52;
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$case float:
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$Rep = uint;
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const EXPONENT_BITS = 8;
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const SIGNIFICANT_BITS = 23;
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$case float16:
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$Rep = ushort;
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const EXPONENT_BITS = 5;
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const SIGNIFICANT_BITS = 10;
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$case float128:
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$Rep = uint128;
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const EXPONENT_BITS = 15;
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const SIGNIFICANT_BITS = 112;
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$endswitch
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const $Rep MAX_EXPONENT = ($Rep)1 << EXPONENT_BITS - 1u;
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const $Rep EXPONENT_BIAS = MAX_EXPONENT >> 1u;
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const $Rep ONE_REP = EXPONENT_BIAS << SIGNIFICANT_BITS;
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const $Rep SIGN_BIT = ($Rep)1 << (EXPONENT_BITS + SIGNIFICANT_BITS);
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const $Rep ABS_MASK = SIGN_BIT - 1u;
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const $Rep IMPLICIT_BIT = ($Rep)1 << SIGNIFICANT_BITS;
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const $Rep SIGNIFICANT_MASK = IMPLICIT_BIT - 1u;
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const $Rep EXPONENT_MASK = ABS_MASK ^ SIGNIFICANT_MASK;
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const $Rep QUIET_BIT = IMPLICIT_BIT >> 1;
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const $Rep QNAN_REP = EXPONENT_MASK | QUIET_BIT;
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const $Rep INF_REP = EXPONENT_MASK;
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$Rep rep = bitcast(a, $Rep);
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$Rep abs = rep & ABS_MASK;
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int sign = rep & SIGN_BIT ? -1 : 1;
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int exponent = (int)((abs >> SIGNIFICANT_BITS) - EXPONENT_BIAS);
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$Rep significand = (abs & SIGNIFICANT_MASK) | IMPLICIT_BIT;
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if (exponent < 0) return 0;
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if ((uint)exponent >= uint128.sizeof * 8) return sign == 1 ? int128.max : int128.min;
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if (exponent < SIGNIFICANT_BITS) return sign * ((int128)significand >> (SIGNIFICANT_BITS - exponent));
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return sign * ((int128)significand << (exponent - SIGNIFICANT_BITS));
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}
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